Compressor rotor blade airfoils

ABSTRACT

A rotor blade includes an airfoil having an airfoil shape. The airfoil shape has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value. The airfoil profile sections at Z values are joined smoothly with one another to form a complete airfoil shape.

FIELD

The present disclosure relates to an airfoil for a compressor rotor blade disposed within a stage of a compressor section of a land-based gas turbine system and, more particularly, relates to a shape defining a profile for an airfoil of a compressor rotor blade.

BACKGROUND

Some simple cycle or combined cycle power plant systems employ turbomachines in their design and operation. Generally, turbomachines employ airfoils (e.g., stator vanes or nozzles and rotor blades), which during operation are exposed to fluid flows. These airfoils are configured to aerodynamically interact with the fluid flows and to transfer energy to or from these fluid flows as part of power generation. For example, the airfoils may be used to compress fluid, create thrust, to convert kinetic energy to mechanical energy, and/or to convert thermal energy to mechanical energy. As a result of this interaction and conversion, the aerodynamic characteristics of these airfoils may result in losses that have an impact on system and turbine operation, performance, thrust, efficiency, and power.

BRIEF DESCRIPTION

Aspects and advantages of the rotor blades and turbomachines in accordance with the present disclosure will be set forth in part in the following description, or may be obvious from the description, or may be learned through practice of the technology.

In accordance with one embodiment, a rotor blade is provided. A rotor blade includes an airfoil having an airfoil shape. The airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance. The X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value. The airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape.

The airfoil shape (e.g., the airfoil shape 150 in FIGS. 3 and 4) has a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I. Table I defines a plurality of airfoil profile sections of the airfoil (e.g., the airfoil 100 in FIGS. 3 and 4) at respective Z-positions. For each airfoil profile section of the airfoil at each Z position, the points defined by the X and Y coordinates are connected together by smooth continuing arcs thereby to define the shape of that airfoil profile section. Also, adjacent airfoil profile sections along the Z-direction are connected together by smooth continuing surfaces. Thus, the complete airfoil shape is defined. Advantageously, this airfoil shape tends to provide for improved aerodynamic efficiency of the airfoil when compared to conventional airfoil designs.

In accordance with another embodiment, a rotor blade is provided. The rotor blade includes an airfoil having a nominal suction-side profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance. The X and Y values, when connected by smooth continuing arcs, define suction-side profile sections at each Z value. The suction-side profile sections at the Z values being joined smoothly with one another to form a complete airfoil suction-side shape.

In accordance with yet another embodiment, a turbomachine is provided. The turbomachine includes a compressor section, a turbine section downstream from the compressor section, and a combustion section downstream from the compressor section and upstream from the turbine section. A rotor blade is disposed within one of the compressor section or the turbine section. The rotor blade includes an airfoil having a nominal suction-side profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I. The Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance. The X and Y values, when connected by smooth continuing arcs, define suction-side profile sections at each Z value. The suction-side profile sections at the Z values being joined smoothly with one another to form a complete airfoil suction-side shape.

These and other features, aspects and advantages of the present rotor blades and turbomachines will become better understood with reference to the following description and appended claims. The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments of the technology and, together with the description, serve to explain the principles of the technology.

BRIEF DESCRIPTION OF THE DRAWINGS

A full and enabling disclosure of the present rotor blades and turbomachines, including the best mode of making and using the present systems and methods, directed to one of ordinary skill in the art, is set forth in the specification, which makes reference to the appended figures, in which:

FIG. 1 is a schematic illustration of a turbomachine in accordance with embodiments of the present disclosure;

FIG. 2 illustrates a cross-sectional side view of a compressor section, in accordance with embodiments of the present disclosure;

FIG. 3 illustrates a perspective view of a rotor blade, in accordance with embodiments of the present disclosure;

FIG. 4 illustrates an airfoil profile section of an airfoil from along the line 4-4 shown in FIG. 3, in accordance with embodiments of the present disclosure; and

FIG. 5 illustrates a graph of a stagger angle distribution belonging to an airfoil disposed on a rotor blade within a specified stage of a compressor section, in accordance with embodiments of the present disclosure.

DETAILED DESCRIPTION

Reference now will be made in detail to embodiments of the present rotor blades and turbomachines, one or more examples of which are illustrated in the drawings. Each example is provided by way of explanation, rather than limitation of, the technology. In fact, it will be apparent to those skilled in the art that modifications and variations can be made in the present technology without departing from the scope or spirit of the claimed technology. For instance, features illustrated or described as part of one embodiment can be used with another embodiment to yield a still further embodiment. Thus, it is intended that the present disclosure covers such modifications and variations as come within the scope of the appended claims and their equivalents.

The detailed description uses numerical and letter designations to refer to features in the drawings. Like or similar designations in the drawings and description have been used to refer to like or similar parts of the invention. As used herein, the terms “first”, “second”, and “third” may be used interchangeably to distinguish one component from another and are not intended to signify location or importance of the individual components.

As used herein, the terms “upstream” (or “forward”) and “downstream” (or “aft”) refer to the relative direction with respect to fluid flow in a fluid pathway. For example, “upstream” refers to the direction from which the fluid flows, and “downstream” refers to the direction to which the fluid flows. The term “radially” refers to the relative direction that is substantially perpendicular to an axial centerline of a particular component, the term “axially” refers to the relative direction that is substantially parallel and/or coaxially aligned to an axial centerline of a particular component and the term “circumferentially” refers to the relative direction that extends around the axial centerline of a particular component. Terms of approximation, such as “generally,” “substantially,” or “about” include values within ten percent greater or less than the stated value. When used in the context of an angle or direction, such terms include within ten degrees greater or less than the stated angle or direction. For example, “generally vertical” includes directions within ten degrees of vertical in any direction, e.g., clockwise or counter-clockwise.

Referring now to the drawings, FIG. 1 illustrates a schematic diagram of one embodiment of a turbomachine, which in the illustrated embodiment is a gas turbine 10. Although an industrial or land-based gas turbine is shown and described herein, the present disclosure is not limited to a land based and/or industrial gas turbine unless otherwise specified in the claims. For example, the invention as described herein may be used in any type of turbomachine including but not limited to a steam turbine, an aircraft gas turbine, or a marine gas turbine.

As shown, gas turbine 10 generally includes an inlet section 12, a compressor section 14 disposed downstream of the inlet section 12, a plurality of combustors (not shown) within a combustor section 16 disposed downstream of the compressor section 14, a turbine section 18 disposed downstream of the combustor section 16, and an exhaust section 20 disposed downstream of the turbine section 18. Additionally, the gas turbine 10 may include one or more shafts 22 coupled between the compressor section 14 and the turbine section 18.

The multi-stage axial compressor section or compressor section 14 may generally include a plurality of rotor disks 24 (one of which is shown) and a plurality of rotor blades 44 extending radially outwardly from and connected to each rotor disk 24. Each rotor disk 24 in turn may be coupled to or form a portion of the shaft 22 that extends through the compressor section 14. The compressor section 14 may further include one or more stator vanes 50 arranged circumferentially around the shaft 22. The stator vanes 50 may be fixed to a static casing or compressor casing 48 that extends circumferentially around the rotor blades 44.

The turbine section 18 may generally include a plurality of rotor disks 28 (one of which is shown) and a plurality of rotor blades 30 extending radially outwardly from and being interconnected to each rotor disk 28. Each rotor disk 28 in turn may be coupled to or form a portion of the shaft 22 that extends through the turbine section 18. The turbine section 18 further includes a turbine casing 33 that circumferentially surround the portion of the shaft 22 and the rotor blades 30, thereby at least partially defining a hot gas path 32 through the turbine section 18. The turbine casing 33 may be configured to support a plurality of stages of stationary nozzles 29 extending radially inwardly from the inner circumference of the turbine casing 33.

During operation, a working fluid such as air flows through the inlet section 12 and into the compressor section 14 where the air is progressively compressed, thus providing pressurized air to the combustors of the combustor section 16. The pressurized air is mixed with fuel and burned within each combustor to produce combustion gases 34. The combustion gases 34 flow through the hot gas path 32 from the combustor section 16 into the turbine section 18, wherein energy (kinetic and/or thermal) is transferred from the combustion gases 34 to the rotor blades 30, causing the shaft 22 to rotate. The mechanical rotational energy may then be used to power the compressor section 14 and/or to generate electricity. The combustion gases 34 exiting the turbine section 18 may then be exhausted from the gas turbine 10 via the exhaust section 20.

FIG. 2 illustrates a cross-sectional side view of an embodiment of the compressor section 14 of the gas turbine 10 of FIG. 1, which is shown as a multi-stage axial compressor section 14, in accordance with embodiments of the present disclosure. As shown in FIGS. 1 and 2, the gas turbine 10 may define a cylindrical coordinate system. The cylindrical coordinate system may define an axial direction A (e.g. downstream direction) substantially parallel to and/or along an axial centerline 23 of the gas turbine 10, a radial direction R perpendicular to the axial centerline 23, and a circumferential direction C extending around the axial centerline 23.

In operation, air 15 may enter the compressor section 14 in the axial direction A through the inlet section 12 and may be pressurized in the multi-stage axial compressor section 14. The compressed air may then be mixed with fuel for combustion within the combustor section 16 to drive the turbine section 18, which rotates the shaft 22 in the circumferential direction C and, thus, the multi-stage axial compressor section 14. The rotation of the shaft 22 also causes one or more rotor blades 44 (e.g., compressor rotor blades) within the multi-stage axial compressor section 14 to draw in and pressurize the air received by the inlet section 12.

The multi-stage axial compressor section 14 may include a rotor assembly 46 having a plurality of rotor disks 24. Rotor blades 44 may extend radially outward from the rotor disks 24. The entire rotor assembly 46 (e.g. rotor disks 24 and rotor blades 44) may rotate in the circumferential direction C during operation of the gas turbine 10. The rotor assembly 46 may be surrounded by a compressor casing 48. The compressor casing may be static or stationary, such that the rotor assembly 46 rotates relative to the compressor casing 48. Stator vanes 50 (e.g., variable stator vanes and/or fixed stator vanes) may extend radially inward from the compressor casing 48. As shown in FIG. 2, one or more stages of the stator vanes 50 may be variable stator vanes 51, such that an angle of the stator vane 50 may be selectively actuated (e.g. by a controller 200). For example, in the embodiments shown in FIG. 2, first three stages of the compressor section 14 may include variable stator vanes 51. In many embodiments, as shown, the rotor blades 44 and stator vanes 50 may be arranged in an alternating fashion, such that most of the rotor blades 44 are disposed between two stator vanes 50 in the axial direction A.

In some embodiments, the compressor casing 48 of the compressor section 14 or the inlet section 12 may have one or more sets of inlet guide vanes 52 (IGVs) (e.g., variable IGV stator vanes). The inlet guide vanes 52 may be mounted to the compressor casing 48, spaced apart from one another in the circumferential direction C, and may be operable to control the amount of air 15 that enters the compressor section 14. Additionally, an outlet 56 of the compressor section 14 may have a set of outlet guide vanes 58 (OGVs). The OGVs 58 may be mounted to the compressor casing 48, spaced apart from one another in the circumferential direction C, and may be operable to control the amount of air 15 that exits the compressor section 14.

In exemplary embodiments, as shown in FIG. 2, the variable stator vane 51, the IGVs 52, and the OGVs may each be configured to vary its vane angle relative to the gas flow (e.g. air flow) by rotating the vane 51, 52, 58 about an axis of rotation (e.g., radially oriented vane shaft). However, each variable stator vane 51 (including the IGVs 52 and the OGVs 58) may be otherwise stationary relative to the rotor blades 44. In certain embodiments, the variable stator vanes 51, the IGVs 52, and the OGVs 58 may be coupled to an actuator 19 (e.g., electric drive, pneumatic drive, or hydraulic drive). The actuators 19 may be in operable communication (e.g. electrical communication) with a controller 200. The controller may be operable to selectively vary the vane angle. In other embodiments, all of the stator vanes 50 may be fixed, such that the stator vanes 50 are configured to remain in a fixed angular position (e.g. the vane angle does not vary).

The compressor section 14 may include a plurality of rows or stages arranged in a serial flow order, such as between 2 to 30, 2 to 25, 2 to 20, 2 to 14, or 2 to 10 rows or stages, or any specific number or range therebetween. Each stage may include a plurality of rotor blades 44 circumferentially spaced about the axial centerline 23 and a plurality of stator vanes 50 circumferentially spaced about the axial centerline 23. In each stage, the multi-stage axial compressor section 14 may include 2 to 1000, 5 to 500, or 10 to 100 of circumferentially arranged rotor blades 44, and 2 to 1000, 5 to 500, or 10 to 100 of circumferentially arranged stator vanes 50. In particular, the illustrated embodiment of the multi-stage axial compressor section 14 includes 14 stages (e.g. S1-S14).

It may be appreciated that each stage has a set of rotor blades 44 disposed at a first axial position and a set of stator vanes 50 disposed at a second axial position along the length of the compressor section 14. In other words, each stage has the rotor blades 44 and stator vanes 50 axially offset from one another, such that the compressor section 14 has an alternating arrangement of rotor blades 44 and stator vanes 50 one set after another along the length of the compressor section 14. Each set of rotor blades 44 extends (e.g., in a spaced arrangement) in the circumferential direction C about the shaft 22, and each set of stator vanes 50 extends (e.g., in a spaced arrangement) in the circumferential direction C within the compressor casing 48.

While the compressor section 14 may include greater or fewer stages than is illustrated, FIG. 2 illustrates an embodiment of the compressor section 14 having fourteen stages arranged in a serial flow order and identified as follows: first stage S1, second stage S2, third stage S3, fourth stage S4, fifth stage S5, sixth stage S6, seventh stage S7, eighth stage S8, ninth stage S9, tenth stage S10, eleventh stage S11, twelfth stage S12, thirteenth stage S13, and fourteenth stage S14. In certain embodiments, each stage may include rotor blades 44 and stator vanes 50 (e.g., fixed stator vanes 50 and/or variable stator vanes 51). As used herein, a rotor blade 44 disposed within one of the sections S1-S14 of the compressor section 14 may be referred to by whichever stage it is disposed within, e.g. “a first stage compressor rotor blade,” “a second stage compressor rotor blade,” “a third stage compressor rotor blade,” etc.

In use, the rotor blades 44 may rotate circumferentially about the compressor casing 48 and the stator vanes 50. Rotation of the rotor blades 44 may result in air entering the inlet section 12. The air is then subsequently compressed as it traverses the various stages (e.g., first stage S1 to fourteenth stage S14) of the compressor section 14 and moves in the axial direction 38 downstream of the multi-stage axial compressor section 14. The compressed air may then exit through the outlet 56 of the multi-stage axial compressor section 14. As discussed above, the outlet 56 may have a set of outlet guide vanes 58 (OGVs). The compressed air that exits the compressor section 14 may be mixed with fuel, directed to the combustor section 16, directed to the turbine section 18, or elsewhere in the gas turbine 10.

TABLE I below contains coordinate data that describes a respective airfoil shape (or surface profile). In exemplary embodiments, the airfoil shapes defined by TABLE I describe an airfoil 100 belonging to a rotor blade 44 and/or a stator vane 50 of the compressor section 14. In certain embodiments, the airfoil shapes defined by TABLE I describe an IGV 52 and/or an OGV 58 of the compressor section 14.

The IGV 52, the stages (e.g. S1-S14) of rotor blades 44 and stator vanes 50, and the OGV 58 of the compressor section 14 may be grouped into one or more sections or portions of the compressor section 14 for reference purposes. For the purposes of the grouping, portions the compressor section 14 may be expressed in terms of a percentage, such as a percentage of the compressor section 14 from the inlet (e.g. 0% of the compressor section 14) to the outlet (e.g. 100% of the compressor section 14) in the axial or downstream direction. In this way, the compressor section 14 may include, in a serial flow order, an early stage 60, a mid stage 62, and a late stage 64. In particular, the early stage 60 may include from approximately 0% to approximately 25% of the compressor section 14 (e.g. from the IGV 52 to about the fourth stage S4). The mid stage 62 may include from approximately 25% to approximately 75% of the compressor section 14 (e.g. from about the fifth stage S5 to about the eleventh stage S11). The late stage 64 may include from approximately 75% to approximately 100% of the compressor section 14 (e.g. from about the twelfth stage S12 to the OGV 58).

Accordingly, the Cartesian coordinate data contained in TABLE I may correspond to an airfoil shape of an airfoil 100 disposed within the early stage 60 of the compressor section 14. For example, in exemplary embodiments, the Cartesian coordinate data contained within TABLE I may correspond to an airfoil shape of an airfoil 100 disposed on a rotor blade 44 in the first stage S1 of the compressor section 14.

However, in various other embodiments, TABLE I may contain Cartesian coordinate data of an airfoil shape of an airfoil 100 that may be disposed on a rotor blade 44 or stator blade 50 in any stage S1-S14 of the compressor section 14. Accordingly, the airfoil shape defined by TABLE I should not be limited to any particular stage of the compressor section 14 unless specifically recited in the claims.

FIG. 3 illustrates a perspective view of a rotor blade 44, which may be incorporated in any stage (e.g. S1 through S14) of the compressor section 14, in accordance with embodiments of the present disclosure.

As shown, the rotor blade 44 includes an airfoil 100 defining an airfoil shape 150. The airfoil 100 includes a pressure-side surface or profile 102 and an opposing suction-side surface or profile 104. The pressure-side surface 102 and the suction-side surface 104 meet or intersect at a leading edge 106 and a trailing edge 108 of the airfoil 100. A chord line 110 extends between the leading edge 106 and the trailing edge 108 such that pressure and suction-side surfaces 102, 104 can be said to extend in chord or chordwise between the leading edge 106 and the trailing edge 108. The leading and trailing edges, 106 and 108 respectively, may be described as the dividing or intersecting lines between the suction-side surface 104 and the pressure-side surface 102. In other words, the suction-side surface 104 and the pressure-side surface 102 couple together with one another along the leading edge 106 and the trailing edge 108, thereby defining an airfoil shaped cross-section that gradually changes lengthwise along the airfoil 100.

In operation, the rotor blades 44 rotate about an axial centerline 23 exerting a torque on a working fluid, such as air 15, thus increasing energy levels of the fluid as the working fluid traverses the various stages S1 through S14 of the multi-stage axial compressor section 14 on its way to the combustor 26. The rotor blades 44 may be adjacent (e.g., upstream and/or downstream) to the one or more stationary stator vanes 50. The stator vanes 50 slow the working fluid during rotation of the rotor blades 44, converting a circumferential component of movement of the working fluid flow into pressure. Accordingly, continuous rotation of the rotor blade 44 creates a continuous flow of compressed working fluid, suitable for combustion via the combustor 26.

As shown in FIG. 3, the airfoil 100 includes a root or first end 112, which intersects with and extends radially outwardly from a base or platform 114 of the rotor blade 44. The airfoil 100 terminates radially at a second end or radial tip 116 of the airfoil 100. The pressure-side and suction-side surfaces 102, 104 can be said to extend in span or in a span-wise direction 118 between the root 112 and/or the platform 114 and the radial tip 116 of the airfoil 100. In other words, each rotor blade 44 includes an airfoil 100 having opposing pressure-side and suction-side surfaces 102, 104 that extend in chord or chordwise 110 between opposing leading and trailing edges 106, 108 and that extend in span or span-wise 118 between the root 112 and the radial tip 116 of the airfoil 100.

In particular configurations, the airfoil 100 may include a fillet 72 formed between the platform 114 and the airfoil 100 proximate to the root 112. The fillet 72 can include a weld or braze fillet, which can be formed via conventional MIG welding, TIG welding, brazing, etc., and can include a profile that can reduce fluid dynamic losses as a result of the presence of fillet 72. In particular embodiments, the platform 114, the airfoil 100 and the fillet 72 can be formed as a single component, such as by casting and/or machining and/or additive manufacturing (such as 3D printing) and/or any other suitable technique now known or later developed and/or discovered.

In various implementations, the rotor blade 44 includes a mounting portion 74 (such as a dovetail joint), which is formed to connect and/or to secure the rotor blade 44 to the rotor disk 24. For example, the mounting portion 74 may include a T-shaped structure, a hook, one or more lateral protrusions, one or more lateral slots, or any combination thereof. The mounting portion 74 (e.g., dovetail joint) may be configured to mount into the rotor assembly 46 or the compressor casing 48 in an axial direction A, a radial direction R, and/or a circumferential direction C (e.g., into an axial slot or opening, a radial slot or opening, and/or a circumferential slot or opening).

An important term in this disclosure is “profile”. The profile is the range of the variation between measured points on an airfoil surface and the ideal position listed in TABLE I. The actual profile on a manufactured turbine rotor blade will be different than those in TABLE I, and the design is robust to this variation meaning that mechanical and aerodynamic function are not impaired. As noted above, a + or −5% profile tolerance is used herein. The X, Y and Z values are all non-dimensionalized relative to the airfoil height.

The airfoil 100 of the rotor blade 44 has a nominal profile at any cross-section taken between the platform 114 or the root 112 and the radial tip 116, e.g., such as the cross section shown in FIG. 4. A “nominal profile” is the range of variation between measured points on an airfoil surface and the ideal position listed in TABLE I. The actual profile on a manufactured compressor blade may be different from those in TABLE I (e.g., due to manufacturing tolerances), and the design is robust to this variation, meaning that mechanical and aerodynamic function are not impaired.

The Cartesian coordinate values of X, Y, and Z provided in TABLE I are dimensionless values scalable by a scaling factor, as measured in any given unit of distance (e.g., inches). For example, the X, Y, and Z values in TABLE I are set forth in non-dimensionalized units, and thus a variety of units of dimensions may be used when the values are appropriately scaled by a scaling factor. As one example only, the Cartesian coordinate values of X, Y and Z may be convertible to dimensional distances by multiplying the X, Y and Z values by a scaling factor. The scaling factor may be substantially equal to 1, greater than 1, or less than 1. For example, the Cartesian coordinate values of X, Y, and Z may be convertible to dimensional distances by multiplying the X, Y, and Z values by the scaling factor. The scaling factor, used to convert the non-dimensional values to dimensional distances, may be a fraction (e.g., ½, %, etc.), decimal fraction (e.g., 0.5, 1.5, 10.25, etc.), integer (e.g., 1, 2, 10, 100, etc.) or a mixed number (e.g., 1½, 10¼, etc.). The scaling factor may be a dimensional distance in any suitable format (e.g., inches, feet, millimeters, centimeters, etc.). In various embodiments, the scaling factor may be between about 0.01 inches and about 10 inches, such as between about 0.1 inches and about 10 inches, such as between about 0.1 inches and about 5 inches, such as between about 0.1 inches and about 3 inches, such as between about 0.1 inches and about 2 inches.

In various embodiments, the X, Y, and Z values in TABLE I may be scaled as a function of the same scaling factor (e.g., constant or number) to provide a scaled-up or a scaled-down airfoil. In this way, TABLE I defines the relationships between the respective X, Y, and Z coordinate values without specifying the units of measure (e.g., dimensional units) for the various airfoil 100 embodiments. Accordingly, while different scaling factors may be applied to the respective X, Y, and Z coordinate values of TABLE I to define different embodiments of the airfoil 100, each embodiment of the airfoil 100 regardless of the particular scaling factor is considered to be defined by the respective X, Y, and Z coordinate values of TABLE I. For example, the X, Y, and Z coordinate values of TABLE I may each define an embodiment of the airfoil 100 formed with a 1:1 inch scaling factor, or formed with a 1:2 inch scaling factor, or formed with a 1:1 cm scaling factor. It may be appreciated that any scaling factor may be used with the X, Y, and Z coordinate values of TABLE I, according to the design considerations of a particular embodiment.

A gas turbine hot gas path requires airfoils that meet system requirements of aerodynamic and mechanical blade loading and efficiency. To define the airfoil shape of each compressor rotor blade airfoil, there is a unique set or loci of points in space that meet the stage requirements and that can be manufactured. This unique loci of points meet the requirements for stage efficiency and are arrived at by iteration between aerodynamic and mechanical loadings enabling the turbine to nm in an efficient, safe and smooth manner. These points are unique and specific to the system.

The loci that define the compressor rotor blade airfoil shape include a set of points with X, Y and Z dimensions relative to a reference origin coordinate system. The Cartesian coordinate system of X, Y and Z values given in TABLE I below defines the airfoil shapes (which include the various airfoil profile sections) of an airfoil belonging to one or more compressor rotor blades or compressor stator vanes at various locations along its height (or along the span-wise direction 118).

TABLE I lists data for an uncoated airfoil at cold or room temperature. The envelope/tolerance for the coordinates is about +/−5% in a direction normal to any airfoil surface location and/or about +/−5% of the chord 110 in a direction nominal to any airfoil surface location. In other words, the airfoil layout, as embodied by the disclosure, is robust to this range of variation without impairment of mechanical and aerodynamic functions. As used herein, the term of approximation “substantially,” when used in the phrase “substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I,” refers to the envelope/tolerance for the coordinates (e.g., +/−5% in a direction nominal to any airfoil surface location and/or about +/−5% of the chord 110 in a direction nominal to any airfoil surface location).

A point data origin 76 is defined at the base 114 of the airfoil 100. For example, the point data origin 76 may be defined at the root 112 of the airfoil 100. For example, in some embodiments, the point data origin 76 may be defined at the root 112 of the airfoil 100 at the intersection of a stacking axis (e.g. a radially extending axis) and the compressed air flowpath (e.g. a flowpath of air along the surface of the airfoil). In the embodiments presented in TABLE I below, the point data origin 76 is defined at a transition or intersection line 78 defined between the fillet 72 and the airfoil 100. The point data origin 76 corresponds to the non-dimensional Z value equal to 0.

As described above, the Cartesian coordinate system has orthogonally-related (e.g. mutually orthogonal) X, Y and Z axes, and the X axis lies generally parallel to a axial centerline 23 of the shaft 22, i.e., the rotary axis, and a positive X coordinate value is axial toward an aft, i.e., exhaust, end of the gas turbine 10. The positive Y coordinate value extends from the suction-side surface 104 towards the pressure-side surface 102, and the positive Z coordinate value is radially outwardly from the base 114 toward the radial tip 116. All the values in TABLE I are given at room temperature and do not include the fillet 72 or coatings (not shown).

By defining X and Y coordinate values at selected locations in a Z direction normal to the X, Y plane, an airfoil profile section 160 of the airfoil 100 of the rotor blade 44 may be defined at each Z distance along the length of the airfoil 100. By connecting the X and Y values with smooth continuing arcs, each airfoil profile section of the airfoil 100 at each distance Z may be fixed. The complete airfoil shape 150 may be determined by smoothly connecting the adjacent profile sections to one another.

The values of TABLE I are generated and shown to three decimal places for determining the airfoil shape 150 of the airfoil 100. As the rotor blade 44 heats up during operation of the gas turbine 10, surface stress and temperature will cause a change in the X, Y and Z values. Accordingly, the values for the various airfoil profile sections given in TABLE I define the “nominal” airfoil profile, that is, the profile of an uncoated airfoil at ambient, non-operating or non-hot conditions (e.g., room temperature).

There are typical manufacturing tolerances as well as coatings which must be accounted for in the actual profile of the airfoil 100. Each cross-section is joined smoothly with the other cross-sections to form the complete airfoil shape. It will therefore be appreciated that +/− typical manufacturing tolerances, i.e., +/− values, including any coating thicknesses, are additive to the X and Y values given in TABLE I below. Accordingly, a distance of +/−5% in a direction normal to any surface location along the airfoil profile defines an airfoil profile envelope for this particular rotor blade 44 airfoil design, i.e., a range of variation between measured points on the actual airfoil surface at nominal cold or room temperature and the ideal position of those points as given in TABLE I below at the same temperature. The data provided in TABLE I is scalable (i.e., by a uniform geometric scaling factor), and the geometry pertains to all aerodynamic scales, at, above and/or below 3000 RPM. The design of the airfoil 100 for rotor blade 44 is robust to this range of variation without impairment of mechanical and aerodynamic functions.

The airfoil 100 may include various airfoil profile sections along the span-wise direction 118. Each of the airfoil profile sections may be “stacked” on top of one another other along the Z direction, such that when connected with smooth continuous arcs, the complete airfoil shape 150 may be ascertained. For example, each airfoil profile section corresponds to Cartesian coordinate values of X, Y, and Z for a common Cartesian coordinate value of Z in TABLE I. Furthermore, adjacent airfoil profile sections correspond to the Cartesian coordinate values of X, Y, and Z for adjacent Cartesian coordinate values of Z in TABLE I.

For example, FIG. 4 illustrates an airfoil profile section 160 of an airfoil 100 from along the line 4-4 shown in FIG. 3, which may be representative of an airfoil profile section of the airfoil 100 at any span-wise location, in accordance with embodiments of the present disclosure. As should be appreciated, the airfoil shape 150 of the airfoil 100 may change or vary at each span-wise location (or at each Z value). In this way, a distinct airfoil profile section 160 may be defined at each position along the span-wise direction 118 (or at each Z value) of the airfoil 100. When the airfoil profile sections 160 at each span-wise location (e.g. at each Z value) of the airfoil 100 are connected together with smooth continuous lines, the complete airfoil shape 150 of the airfoil 100 may be defined or obtained.

A Cartesian coordinate system of X, Y, and Z values given in TABLE I below define respective suction side surfaces or profiles 104 and a pressure side surfaces or profiles 102 of the respective airfoils 100 at various locations along the span-wise direction 118 of the respective airfoils 100. For example, point 120 defines a first pair of suction side X and Y values at the Z value of the airfoil profile section 160 shown in FIG. 4 (line 4-4 shown in FIG. 3), while point 122 defines a second pair of pressure side X and Y values at the same Z value.

By defining X and Y coordinate values at selected locations in a Z direction normal to the X-Y plane, an airfoil profile section 160 of the airfoil 100 may be obtained at each of the selected Z value location (e.g. by connecting each X and Y coordinate value at a given Z value to adjacent X and Y coordinate values of that same Z value with smooth continuing arcs). At each Z value or location, the suction side profile 104 may joined to the pressure-side profile or surface 102, as shown in FIG. 4, to define the airfoil profile section 160. The airfoil shape 150 of the airfoil 100 may be determined by smoothly connecting the adjacent (e.g., “stacked”) airfoil profile sections 160 to one another with smooth continuous arcs.

The values in TABLE I below are computer-generated and shown to three decimal places. However, certain values in TABLE I may be shown to less than five decimal places (e.g., 0, 1, or 2 decimal places), because the values are rounded to significant figures, the additional decimal places would merely show trailing zeroes, or a combination thereof. Accordingly, in certain embodiments, any values having less than three decimal places may be shown with trailing zeroes out to 1, 2, or 3 decimal places. Furthermore, in some embodiments and in view of manufacturing constraints, actual values useful for forming the airfoil 100 are may be considered valid to fewer than three decimal places for determining the airfoil shape 150 of the airfoil 100.

As will be appreciated, there are typical manufacturing tolerances which may be accounted for in the airfoil shape 150. Accordingly, the X, Y, and Z values given in TABLE I are for the airfoil shape 150 of a nominal airfoil. It will therefore be appreciated that plus or minus typical manufacturing tolerances (e.g. plus or minus 5%) are applicable to these X, Y, and Z values and that an airfoil 100 having a profile substantially in accordance with those values includes such tolerances.

As noted previously, the airfoil 100 may also be coated for protection against corrosion, erosion, wear, and oxidation after the airfoil 100 is manufactured, according to the values in TABLE I and within the tolerances explained above. For example, the coating region may include one or more corrosion resistant layers, erosion resistant layers, wear resistant layers, oxidation resistant or anti-oxidation layers, or any combination thereof. For example, in embodiments where the airfoil is measured in inches, an anti-corrosion coating may be provided with an average thickness t of 0.008 inches (0.20 mm), between 0.001 and 0.1 inches (between 0.025 and 2.5 mm), or between 0.0001 and 0.5 inches or more (between 0.0025 and 12.7 mm or more). For example, in certain embodiments, the coating may increase X and Y values of a suction side in TABLE I by no greater than approximately 3.5 mm along a first suction portion, a first pressure portion, or both. It is to be noted that additional anti-oxidation coatings may be provided, such as overcoats. The values provided in TABLE I exclude a coated region or coatings of the airfoil 100. In other words, these values correspond to the bare surface of the airfoil 100. The coated region may include one or more coating layers, surface treatments, or a combination thereof, over the bare surface of the airfoil 100.

TABLE I below contains Cartesian coordinate data of an airfoil shape 150 of an airfoil 100, which may be incorporated into one of the compressor section 14 or the turbine section 18 of the gas turbine 10. For example, in many embodiments, TABLE I below contains Cartesian coordinate data of an airfoil shape 150 of an airfoil 100 of a rotor blade 44, which is disposed in one of the early stage 60, the mid stage 62, or the late stage 64 of the compressor section 14 (such as in any one of stages S1-S14).

In exemplary embodiments, TABLE I below contains Cartesian coordinate data of an airfoil shape 150 of an airfoil 100 of a rotor blade 44, which is disposed in the early stage 60 of the compressor section 14. Specifically, TABLE I below contains Cartesian coordinate data of an airfoil shape 150 of an airfoil 100 of a rotor blade 44, which is disposed in the first stage S51 of the compressor section 14.

TABLE I SUCTION SIDE PRESSURE SIDE X Y Z X Y Z 11.554 −4.259 5.194 −10.193 8.169 5.194 11.553 −4.266 5.194 −10.188 8.172 5.194 11.548 −4.279 5.194 −10.179 8.177 5.194 11.534 −4.308 5.194 −10.160 8.181 5.194 11.499 −4.347 5.194 −10.119 8.176 5.194 11.415 −4.385 5.194 −10.060 8.154 5.194 11.296 −4.384 5.194 −9.961 8.097 5.194 11.136 −4.377 5.194 −9.837 8.007 5.194 10.924 −4.368 5.194 −9.682 7.876 5.194 10.658 −4.355 5.194 −9.495 7.703 5.194 10.312 −4.337 5.194 −9.258 7.473 5.194 9.914 −4.315 5.194 −8.984 7.207 5.194 9.489 −4.288 5.194 −8.691 6.925 5.194 9.038 −4.256 5.194 −8.358 6.610 5.194 8.534 −4.215 5.194 −7.986 6.264 5.194 7.951 −4.159 5.194 −7.572 5.888 5.194 7.343 −4.090 5.194 −7.132 5.502 5.194 6.710 −4.006 5.194 −6.668 5.105 5.194 6.053 −3.905 5.194 −6.180 4.698 5.194 5.372 −3.782 5.194 −5.667 4.281 5.194 4.669 −3.635 5.194 −5.132 3.850 5.194 3.946 −3.457 5.194 −4.572 3.410 5.194 3.204 −3.246 5.194 −3.987 2.961 5.194 2.445 −2.996 5.194 −3.375 2.506 5.194 1.699 −2.715 5.194 −2.754 2.061 5.194 0.965 −2.400 5.194 −2.125 1.631 5.194 0.246 −2.055 5.194 −1.484 1.216 5.194 −0.460 −1.681 5.194 −0.833 0.818 5.194 −1.151 −1.282 5.194 −0.171 0.438 5.194 −1.827 −0.857 5.194 0.501 0.077 5.194 −2.487 −0.408 5.194 1.182 −0.267 5.194 −3.131 0.063 5.194 1.870 −0.596 5.194 −3.758 0.557 5.194 2.565 −0.911 5.194 −4.369 1.071 5.194 3.264 −1.216 5.194 −4.964 1.603 5.194 3.969 −1.510 5.194 −5.526 2.131 5.194 4.654 −1.782 5.194 −6.057 2.654 5.194 5.320 −2.036 5.194 −6.558 3.168 5.194 5.964 −2.777 5.194 −7.030 3.674 5.194 6.588 −2.492 5.194 −7.473 4.170 5.194 7.189 −2.698 5.194 −7.890 4.654 5.194 7.768 −2.893 5.194 −8.285 5.121 5.194 8.324 −3.076 5.194 −8.656 5.574 5.194 8.855 −3.250 5.194 −8.987 5.991 5.194 9.315 −3.400 5.194 −9.277 6.372 5.194 9.726 −3.534 5.194 −9.529 6.715 5.194 10.113 −3.659 5.194 −9.755 7.044 5.194 10.477 −3.775 5.194 −9.937 7.338 5.194 10.792 −3.875 5.194 −10.065 7.571 5.194 11.034 −3.952 5.194 −10.153 7.765 5.194 11.228 −4.013 5.194 −10.205 7.916 5.194 11.374 −4.058 5.194 −10.228 8.033 5.194 11.482 −4.096 5.194 −10.227 8.100 5.194 11.542 −4.160 5.194 −10.215 8.140 5.194 11.557 −4.208 5.194 −10.204 8.158 5.194 11.558 −4.239 5.194 −10.197 8.166 5.194 11.556 −4.251 5.194 9.530 −5.074 9.543 −9.605 8.402 9.543 9.527 −5.081 9.543 −9.601 8.405 9.543 9.522 −5.092 9.543 −9.592 8.409 9.543 9.507 −5.117 9.543 −9.574 8.411 9.543 9.471 −5.151 9.543 −9.537 8.405 9.543 9.391 −5.178 9.543 −9.483 8.382 9.543 9.283 −5.162 9.543 −9.393 8.325 9.543 9.138 −5.138 9.543 −9.281 8.238 9.543 8.945 −5.104 9.543 −9.140 8.112 9.543 8.705 −5.061 9.543 −8.970 7.947 9.543 8.392 −5.002 9.543 −8.754 7.729 9.543 8.032 −4.931 9.543 −8.504 7.477 9.543 7.650 −4.851 9.543 −8.235 7.210 9.543 7.244 −4.762 9.543 −7.932 6.912 9.543 6.791 −4.655 9.543 −7.591 6.584 9.543 6.270 −4.524 9.543 −7.213 6.228 9.543 5.727 −4.376 9.543 −6.814 5.857 9.543 5.165 −4.208 9.543 −6.396 5.474 9.543 4.584 −4.019 9.543 −5.958 5.077 9.543 3.985 −3.805 9.543 −5.499 4.668 9.543 3.370 −3.565 9.543 −5.077 4.243 9.543 2.740 −3.298 9.543 −4.527 3.805 9.543 2.097 −3.000 9.543 −4.011 3.352 9.543 1.443 −2.667 9.543 −3.476 2.887 9.543 0.802 −2.311 9.543 −2.938 2.425 9.543 0.175 −1.931 9.543 −2.395 1.969 9.543 −0.439 −1.530 9.543 −1.844 1.521 9.543 −1.041 −1.110 9.543 −1.285 1.086 9.543 −1.628 −0.671 9.543 −0.715 0.663 9.543 −2.202 −0.215 9.543 −0.136 0.253 9.543 −2.763 0.259 9.543 0.453 −0.143 9.543 −3.309 0.748 9.543 1.050 −0.525 9.543 −3.843 1.251 9.543 1.654 −0.897 9.543 −4.366 1.766 9.543 2.262 −1.263 9.543 −4.880 2.289 9.543 2.874 −1.621 9.543 −5.369 2.802 9.543 3.470 −1.960 9.543 −5.836 3.303 9.543 4.049 −2.280 9.543 −6.280 3.791 9.543 4.611 −2.583 9.543 −6.702 4.267 9.543 5.156 −2.867 9.543 −7.103 4.728 9.543 5.683 −3.136 9.543 −7.483 5.174 9.543 6.191 −3.388 9.543 −7.845 5.605 9.543 6.680 −3.627 9.543 −8.185 6.022 9.543 7.149 −3.851 9.543 −8.488 6.406 9.543 7.555 −4.042 9.543 −8.756 6.755 9.543 7.920 −4.211 9.543 −8.989 7.069 9.543 8.265 −4.368 9.543 −9.199 7.370 9.543 8.588 −4.513 9.543 −9.368 7.639 9.543 8.868 −4.639 9.543 −9.486 7.853 9.543 9.084 −4.735 9.543 −9.567 8.031 9.543 9.257 −4.812 9.543 −9.615 8.169 9.543 9.387 −4.870 9.543 −9.637 8.277 9.543 9.483 −4.916 9.543 −9.637 8.338 9.543 9.531 −4.981 9.543 −9.626 8.375 9.543 9.538 −5.028 9.543 −9.616 8.392 9.543 9.535 −5.056 9.543 −9.609 8.399 9.543 9.532 −5.068 9.543 7.782 −6.696 15.964 −8.833 9.102 15.964 7.778 −6.702 15.964 −8.829 9.105 15.964 7.772 −6.712 15.964 −8.821 9.108 15.964 7.753 −6.733 15.964 −8.802 9.108 15.964 7.713 −6.758 15.964 −8.767 9.097 15.964 7.633 −6.762 15.964 −8.717 9.068 15.964 7.534 −6.723 15.964 −8.635 9.006 15.964 7.404 −6.669 15.964 −8.533 8.912 15.964 7.231 −6.595 15.964 −8.405 8.780 15.964 7.016 −6.502 15.964 −8.249 8.610 15.964 6.737 −6.377 15.964 −8.050 8.387 15.964 6.417 −6.229 15.964 −7.818 8.130 15.964 6.078 −6.067 15.964 −7.569 7.859 15.964 5.720 −5.889 15.964 −7.285 7.557 15.964 5.323 −5.684 15.964 −6.968 7.223 15.964 4.868 −5.439 15.964 −6.617 6.857 15.964 4.398 −5.173 15.964 −6.249 6.476 15.964 3.913 −4.885 15.964 −5.865 6.079 15.964 3.416 −4.572 15.964 −5.464 5.666 15.964 2.906 −4.235 15.964 −5.047 5.236 15.964 2.386 −3.872 15.964 −4.614 4.789 15.964 1.856 −3.482 15.964 −4.166 4.326 15.964 1.318 −3.063 15.964 −3.703 3.844 15.964 0.775 −2.614 15.964 −3.224 3.346 15.964 0.245 −2.150 15.964 −2.746 2.847 15.964 −0.272 −1.671 15.964 −2.269 2.347 15.964 −0.779 −1.181 15.964 −1.791 1.848 15.964 −1.276 −0.681 15.964 −1.312 1.350 15.964 −1.763 −0.171 15.964 −0.829 0.857 15.964 −2.241 0.347 15.964 −0.340 0.368 15.964 −2.711 0.873 15.964 0.155 −0.114 15.964 −3.175 1.403 15.964 0.657 −0.589 15.964 −3.634 1.938 15.964 1.165 −1.057 15.964 −4.089 2.477 15.964 1.678 −1.520 15.964 −4.540 3.019 15.964 2.192 −1.981 15.964 −4.972 3.545 15.964 2.692 −2.424 15.964 −5.386 4.057 15.964 3.177 −2.849 15.964 −5.783 4.552 15.964 3.648 −3.256 15.964 −6.162 5.031 15.964 4.104 −3.643 15.964 −6.524 5.493 15.964 4.545 −4.013 15.964 −6.870 5.939 15.964 4.971 −4.366 15.964 −7.199 6.367 15.964 5.382 −4.701 15.964 −7.511 6.780 15.964 5.777 −5.018 15.964 −7.790 7.158 15.964 6.120 −5.289 15.964 −8.036 7.502 15.964 6.429 −5.530 15.964 −8.250 7.811 15.964 6.721 −5.754 15.964 −8.445 8.105 15.964 6.996 −5.963 15.964 −8.603 8.366 15.964 7.236 −6.143 15.964 −8.713 8.574 15.964 7.420 −6.281 15.964 −8.790 8.745 15.964 7.568 −6.391 15.964 −8.837 8.878 15.964 7.679 −6.473 15.964 −8.859 8.981 15.964 7.761 −6.536 15.964 −8.861 9.040 15.964 7.797 −6.607 15.964 −8.853 9.077 15.964 7.797 −6.653 15.964 −8.843 9.093 15.964 7.790 −6.679 15.964 −8.837 9.099 15.964 7.785 −6.690 15.964 7.061 −8.575 21.897 −8.298 10.110 21.897 7.056 −8.580 21.897 −8.294 10.112 21.897 7.047 −8.589 21.897 −8.284 10.114 21.897 7.023 −8.606 21.897 −8.265 10.111 21.897 6.976 −8.619 21.897 −8.230 10.094 21.897 6.895 −8.595 21.897 −8.182 10.057 21.897 6.806 −8.530 21.897 −8.104 9.981 21.897 6.688 −8.442 21.897 −8.008 9.872 21.897 6.531 −8.325 21.897 −7.887 9.720 21.897 6.335 −8.177 21.897 −7.741 9.526 21.897 6.081 −7.984 21.897 −7.552 9.274 21.897 5.790 −7.758 21.897 −7.331 8.984 21.897 5.482 −7.515 21.897 −7.091 8.679 21.897 5.158 −7.253 21.897 −6.816 8.340 21.897 4.797 −6.957 21.897 −6.509 7.964 21.897 4.384 −6.610 21.897 −6.172 7.551 21.897 3.957 −6.241 21.897 −5.818 7.119 21.897 3.518 −5.848 21.897 −5.448 6.669 21.897 3.068 −5.432 21.897 −5.061 6.202 21.897 2.606 −4.992 21.897 −4.658 5.716 21.897 2.135 −4.527 21.897 −4.241 5.211 21.897 1.655 −4.035 21.897 −3.809 4.687 21.897 1.169 −3.515 21.897 −3.363 4.143 21.897 0.678 −2.967 21.897 −2.904 3.578 21.897 0.198 −2.409 21.897 −2.447 3.011 21.897 −0.269 −1.841 21.897 −1.993 2.442 21.897 −0.728 −1.265 21.897 −1.542 1.871 21.897 −1.178 −0.682 21.897 −1.093 1.298 21.897 −1.621 −0.095 21.897 −0.645 0.724 21.897 −2.059 0.497 21.897 −0.195 0.152 21.897 −2.494 1.091 21.897 0.257 −0.419 21.897 −2.926 1.686 21.897 0.714 −0.985 21.897 −3.357 2.283 21.897 1.177 −1.547 21.897 −3.786 2.882 21.897 1.642 −2.107 21.897 −4.213 3.481 21.897 2.109 −2.665 21.897 −4.624 4.062 21.897 2.562 −3.204 21.897 −5.018 4.625 21.897 3.000 −3.723 21.897 −5.395 5.169 21.897 3.425 −4.222 21.897 −5.756 5.695 21.897 3.835 −4.701 21.897 −6.101 6.202 21.897 4.230 −5.161 21.897 −6.431 6.690 21.897 4.611 −5.602 21.897 −6.746 7.158 21.897 4.975 −6.025 21.897 −7.043 7.608 21.897 5.325 −6.428 21.897 −7.308 8.022 21.897 5.627 −6.776 21.897 −7.540 8.398 21.897 5.899 −7.087 21.897 −7.742 8.734 21.897 6.155 −7.378 21.897 −7.928 9.052 21.897 6.395 −7.652 21.897 −8.080 9.332 21.897 6.604 −7.888 21.897 −8.186 9.553 21.897 6.764 −8.070 21.897 −8.259 9.735 21.897 6.893 −8.216 21.897 −8.304 9.876 21.897 6.989 −8.325 21.897 −8.325 9.984 21.897 7.062 −8.407 21.897 −8.326 10.045 21.897 7.091 −8.485 21.897 −8.318 10.083 21.897 7.084 −8.533 21.897 −8.309 10.100 21.897 7.072 −8.559 21.897 −8.302 10.107 21.897 7.065 −8.569 21.897 6.238 −11.274 29.351 −7.538 11.753 29.351 6.232 −11.279 29.351 −7.533 11.754 29.351 6.220 −11.285 29.351 −7.577 11.754 29.351 6.189 −11.294 29.351 −7.503 11.745 29.351 6.136 −11.284 29.351 −7.470 11.717 29.351 6.071 −11.217 29.351 −7.426 11.666 29.351 5.997 −11.121 29.351 −7.355 11.569 29.351 5.898 −10.992 29.351 −7.268 11.432 29.351 5.766 −10.821 29.351 −7.159 11.247 29.351 5.601 −10.607 29.351 −7.026 11.013 29.351 5.388 −10.328 29.351 −6.853 10.709 29.351 5.143 −10.006 29.351 −6.650 10.360 29.351 4.883 −9.660 29.351 −6.431 9.990 29.351 4.608 −9.292 29.351 −6.180 9.575 29.351 4.303 −8.879 29.351 −5.899 9.116 29.351 3.952 −8.400 29.351 −5.587 8.613 29.351 3.589 −7.896 29.351 −5.259 8.089 29.351 3.213 −7.368 29.351 −4.914 7.542 29.351 2.826 −6.815 29.351 −4.554 6.975 29.351 2.428 −6.235 29.351 −4.177 6.385 29.351 2.021 −5.630 29.351 −3.785 5.774 29.351 1.604 −4.999 29.351 −3.379 5.139 29.351 1.179 −4.341 29.351 −2.961 4.480 29.351 0.747 −3.655 29.351 −2.530 3.798 29.351 0.323 −2.965 29.351 −2.102 3.113 29.351 −0.095 −2.270 29.351 −1.677 2.427 29.351 −0.509 −1.574 29.351 −1.255 1.739 29.351 −0.919 −0.875 29.351 −0.836 1.049 29.351 −1.327 −0.175 29.351 −0.420 0.357 29.351 −1.732 0.527 29.351 −0.006 −0.335 29.351 −2.136 1.230 29.351 0.408 −1.028 29.351 −2.540 1.932 29.351 0.821 −1.722 29.351 −2.943 2.636 29.351 1.235 −2.415 29.351 −3.344 3.340 29.351 1.648 −3.108 29.351 −3.743 4.045 29.351 2.060 −3.802 29.351 −4.127 4.728 29.351 2.457 −4.474 29.351 −4.496 5.388 29.351 2.839 −5.123 29.351 −4.849 6.026 29.351 3.207 −5.750 29.351 −5.187 6.642 29.351 3.560 −6.354 29.351 −5.511 7.234 29.351 3.897 −6.935 29.351 −5.821 7.804 29.351 4.770 −7.495 29.351 −6.114 8.352 29.351 4.527 −8.032 29.351 −6.391 8.878 29.351 4.820 −8.546 29.351 −6.637 9.359 29.351 5.073 −8.991 29.351 −6.851 9.795 29.351 5.298 −9.389 29.351 −7.036 10.186 29.351 5.509 −9.764 29.351 −7.204 10.555 29.351 5.706 −10.116 29.351 −7.341 10.878 29.351 5.876 −10.422 29.351 −7.437 11.130 29.351 6.006 −10.657 29.351 −7.503 11.336 29.351 6.111 −10.846 29.351 −7.543 11.493 29.351 6.189 −10.987 29.351 −7.563 11.613 29.351 6.248 −11.093 29.351 −7.566 11.680 29.351 6.281 −11.179 29.351 −7.559 11.723 29.351 6.271 −11.232 29.351 −7.550 11.742 29.351 6.254 −11.259 29.351 −7.543 11.750 29.351 6.245 −11.269 29.351 5.378 −12.656 33.390 −6.912 12.645 33.390 5.370 −12.660 33.390 −6.907 12.646 33.390 5.357 −12.665 33.390 −6.896 12.643 33.390 5.324 −12.666 33.390 −6.878 12.630 33.390 5.278 −12.635 33.390 −6.848 12.596 33.390 5.227 −12.550 33.390 −6.807 12.538 33.390 5.163 −12.441 33.390 −6.743 12.429 33.390 5.077 −12.295 33.390 −6.664 12.280 33.390 4.963 −12.100 33.390 −6.564 12.077 33.390 4.821 −11.855 33.390 −6.442 11.823 33.390 4.637 −11.537 33.390 −6.283 11.493 33.390 4.428 −11.169 33.390 −6.098 11.113 33.390 4.205 −10.776 33.390 −5.899 10.708 33.390 3.971 −10.356 33.390 −5.673 10.253 33.390 3.710 −9.887 33.390 −5.419 9.749 33.390 3.410 −9.343 33.390 −5.136 9.197 33.390 3.098 −8.773 33.390 −4.839 8.621 33.390 2.776 −8.176 33.390 −4.526 8.020 33.390 2.446 −7.552 33.390 −4.197 7.397 33.390 2.108 −6.900 33.390 −3.852 6.750 33.390 1.762 −6.220 33.390 −3.492 6.079 33.390 1.407 −5.514 33.390 −3.116 5.385 33.390 1.043 −4.780 33.390 −2.725 4.666 33.390 0.669 −4.019 33.390 −2.323 3.922 33.390 0.297 −3.258 33.390 −1.977 3.177 33.390 −0.075 −2.496 33.390 −1.524 2.431 33.390 −0.448 −1.735 33.390 −1.128 1.683 33.390 −0.823 −0.975 33.390 −0.735 0.934 33.390 −1.201 −0.216 33.390 −0.346 0.183 33.390 −1.579 0.542 33.390 0.038 −0.571 33.390 −1.957 1.300 33.390 0.417 −1.328 33.390 −2.334 2.059 33.390 0.790 −2.087 33.390 −2.710 2.819 33.390 1.158 −2.849 33.390 −3.084 3.579 33.390 1.522 −3.613 33.390 −3.455 4.341 33.390 1.880 −4.379 33.390 −3.812 5.079 33.390 2.777 −5.122 33.390 −4.154 5.792 33.390 2.549 −5.841 33.390 −4.482 6.481 33.390 2.861 −6.535 33.390 −4.794 7.145 33.390 3.160 −7.205 33.390 −5.092 7.786 33.390 3.444 −7.850 33.390 −5.376 8.402 33.390 3.713 −8.471 33.390 −5.643 8.994 33.390 3.968 −9.067 33.390 −5.893 9.563 33.390 4.210 −9.638 33.390 −6.115 10.082 33.390 4.419 −10.132 33.390 −6.308 10.553 33.390 4.605 −10.574 33.390 −6.473 10.973 33.390 4.779 −10.990 33.390 −6.621 11.371 33.390 4.941 −11.381 33.390 −6.741 11.718 33.390 5.079 −11.720 33.390 −6.824 11.988 33.390 5.186 −11.982 33.390 −6.882 12.206 33.390 5.270 −12.191 33.390 −6.918 12.372 33.390 5.334 −12.348 33.390 −6.935 12.498 33.390 5.381 −12.465 33.390 −6.938 12.568 33.390 5.417 −12.557 33.390 −6.933 12.613 33.390 5.412 −12.613 33.390 −6.924 12.634 33.390 5.395 −12.641 33.390 −6.917 12.642 33.390 5.385 −12.651 33.390 4.506 −13.295 36.083 −6.572 13.384 36.083 4.499 −13.298 36.083 −6.566 13.385 36.083 4.485 −13.302 36.083 −6.556 13.380 36.083 4.451 −13.295 36.083 −6.539 13.365 36.083 4.418 −13.249 36.083 −6.511 13.328 36.083 4.371 −13.159 36.083 −6.474 13.265 36.083 4.311 −13.043 36.083 −6.415 13.149 36.083 4.232 −12.888 36.083 −6.343 12.991 36.083 4.127 −12.682 36.083 −6.251 12.778 36.083 3.998 −12.422 36.083 −6.138 12.512 36.083 3.832 −12.084 36.083 −5.989 12.166 36.083 3.645 −11.692 36.083 −5.816 11.768 36.083 3.447 −11.272 36.083 −5.630 11.343 36.083 3.240 −10.825 36.083 −5.420 10.866 36.083 3.009 −10.325 36.083 −5.186 10.337 36.083 2.745 −9.745 36.083 −4.927 9.754 36.083 2.472 −9.137 36.083 −4.654 9.147 36.083 2.193 −8.500 36.083 −4.366 8.515 36.083 1.907 −7.834 36.083 −4.061 7.858 36.083 1.616 −7.139 36.083 −3.743 7.175 36.083 1.319 −6.415 36.083 −3.410 6.468 36.083 1.013 −5.663 36.083 −3.061 5.736 36.083 0.697 −4.884 36.083 −2.698 4.979 36.083 0.368 −4.079 36.083 −2.324 4.195 36.083 0.038 −3.275 36.083 −1.951 3.410 36.083 −0.295 −2.472 36.083 −1.580 2.624 36.083 −0.632 −1.670 36.083 −1.712 1.837 36.083 −0.974 −0.871 36.083 −0.849 1.048 36.083 −1.318 −0.072 36.083 −0.491 0.257 36.083 −1.664 0.725 36.083 −0.139 −0.538 36.083 −2.012 1.522 36.083 0.206 −1.335 36.083 −2.360 2.319 36.083 0.545 −2.135 36.083 −2.707 3.116 36.083 0.876 −2.938 36.083 −3.054 3.914 36.083 1.199 −3.745 36.083 −3.400 4.711 36.083 1.515 −4.554 36.083 −3.731 5.484 36.083 1.813 −5.339 36.083 −4.050 6.230 36.083 2.096 −6.099 36.083 −4.356 6.951 36.083 2.364 −6.833 36.083 −4.646 7.646 36.083 2.618 −7.542 36.083 −4.922 8.316 36.083 2.859 −8.225 36.083 −5.184 8.960 36.083 3.086 −8.882 36.083 −5.430 9.580 36.083 3.301 −9.512 36.083 −5.660 10.174 36.083 3.505 −10.116 36.083 −5.862 10.718 36.083 3.681 −10.637 36.083 −6.035 11.210 36.083 3.839 −11.103 36.083 −6.182 11.650 36.083 3.987 −11.542 36.083 −6.313 12.064 36.083 4.126 −11.954 36.083 −6.420 12.426 36.083 4.244 −12.311 36.083 −6.495 12.706 36.083 4.335 −12.586 36.083 −6.547 12.931 36.083 4.407 −12.807 36.083 −6.579 13.102 36.083 4.461 −12.972 36.083 −6.594 13.232 36.083 4.501 −13.096 36.083 −6.597 13.304 36.083 4.532 −13.192 36.083 −6.592 13.350 36.083 4.539 −13.249 36.083 −6.584 13.372 36.083 4.524 −13.280 36.083 −6.577 13.381 36.083 4.514 −13.290 36.083 3.905 −13.501 37.826 −6.421 13.988 37.826 3.897 −13.505 37.826 −6.415 13.989 37.826 3.882 −13.508 37.826 −6.405 13.983 37.826 3.850 −13.497 37.826 −6.389 13.966 37.826 3.819 −13.447 37.826 −6.363 13.926 37.826 3.768 −13.357 37.826 −6.329 13.861 37.826 3.705 −13.241 37.826 −6.275 13.741 37.826 3.621 −13.085 37.826 −6.207 13.577 37.826 3.511 −12.876 37.826 −6.121 13.358 37.826 3.378 −12.614 37.826 −6.013 13.085 37.826 3.211 −12.269 37.826 −5.871 12.729 37.826 3.027 −11.868 37.826 −5.705 12.320 37.826 2.835 −11.437 37.826 −5.528 11.884 37.826 2.637 −10.977 37.826 −5.328 11.394 37.826 2.420 −10.461 37.826 −5.107 10.848 37.826 2.175 −9.861 37.826 −4.864 10.248 37.826 1.926 −9.231 37.826 −4.608 9.621 37.826 1.674 −8.570 37.826 −4.337 8.969 37.826 1.420 −7.879 37.826 −4.050 8.292 37.826 1.162 −7.158 37.826 −3.751 7.588 37.826 0.898 −6.408 37.826 −3.437 6.858 37.826 0.626 −5.629 37.826 −3.110 6.101 37.826 0.342 −4.823 37.826 −2.768 5.319 37.826 0.044 −3.991 37.826 −2.416 4.510 37.826 −0.257 −3.161 37.826 −2.066 3.699 37.826 −0.564 −2.332 37.826 −1.718 2.888 37.826 −0.876 −1.505 37.826 −1.373 2.075 37.826 −1.193 −0.680 37.826 −1.033 1.260 37.826 −1.513 0.144 37.826 −0.698 0.444 37.826 −1.834 0.967 37.826 −0.369 −0.376 37.826 −2.157 1.790 37.826 −0.048 −1.198 37.826 −2.481 2.612 37.826 0.266 −2.023 37.826 −2.806 3.434 37.826 0.572 −2.851 37.826 −3.131 4.256 37.826 0.868 −3.683 37.826 −3.455 5.078 37.826 1.155 −4.518 37.826 −3.768 5.873 37.826 1.425 −5.327 37.826 −4.068 6.641 37.826 1.678 −6.111 37.826 −4.357 7.382 37.826 1.916 −6.870 37.826 −4.630 8.098 37.826 2.140 −7.601 37.826 −4.890 8.787 37.826 2.352 −8.306 37.826 −5.136 9.450 37.826 2.552 −8.983 37.826 −5.367 10.086 37.826 2.742 −9.633 37.826 −5.583 10.698 37.826 2.924 −10.254 37.826 −5.770 11.256 37.826 3.084 −10.790 37.826 −5.929 11.762 37.826 3.230 −11.268 37.826 −6.063 12.214 37.826 3.371 −11.717 37.826 −6.182 12.640 37.826 3.505 −12.138 37.826 −6.279 13.010 37.826 3.623 −12.502 37.826 −6.348 13.296 37.826 3.714 −12.782 37.826 −6.396 13.527 37.826 3.788 −13.005 37.826 −6.426 13.701 37.826 3.844 −13.173 37.826 −6.441 13.833 37.826 3.886 −13.298 37.826 −6.444 13.906 37.826 3.919 −13.396 37.826 −6.439 13.953 37.826 3.934 −13.452 37.826 −6.433 13.976 37.826 3.922 −13.485 37.826 −6.426 13.985 37.826 3.912 −13.496 37.826 3.566 −13.328 39.388 −6.332 14.668 39.388 3.558 −13.332 39.388 −6.327 14.668 39.388 3.543 −13.334 39.388 −6.317 14.662 39.388 3.511 −13.321 39.388 −6.302 14.643 39.388 3.480 −13.270 39.388 −6.279 14.602 39.388 3.427 −13.180 39.388 −6.247 14.534 39.388 3.360 −13.064 39.388 −6.197 14.410 39.388 3.271 −12.909 39.388 −6.135 14.243 39.388 3.154 −12.701 39.388 −6.054 14.019 39.388 3.011 −12.439 39.388 −5.952 13.740 39.388 2.832 −12.096 39.388 −5.819 13.377 39.388 2.633 −11.696 39.388 −5.662 12.959 39.388 2.425 −11.266 39.388 −5.493 12.514 39.388 2.210 −10.808 39.388 −5.305 12.013 39.388 1.975 −10.292 39.388 −5.097 11.456 39.388 1.712 −9.691 39.388 −4.870 10.842 39.388 1.451 −9.058 39.388 −4.631 10.202 39.388 1.193 −8.390 39.388 −4.377 9.534 39.388 0.940 −7.689 39.388 −4.110 8.840 39.388 0.691 −6.955 39.388 −3.830 8.120 39.388 0.443 −6.190 39.388 −3.537 7.372 39.388 0.190 −5.395 39.388 −3.231 6.598 39.388 −0.074 −4.571 39.388 −2.913 5.796 39.388 −0.349 −3.721 39.388 −2.583 4.967 39.388 −0.628 −2.871 39.388 −2.255 4.137 39.388 −0.911 −2.023 39.388 −1.930 3.307 39.388 −1.199 −1.176 39.388 −1.608 2.474 39.388 −1.490 −0.331 39.388 −1.291 1.641 39.388 −1.785 0.514 39.388 −0.980 0.805 39.388 −2.082 1.357 39.388 −0.674 −0.034 39.388 −2.382 2.199 39.388 −0.376 −0.875 39.388 −2.684 3.041 39.388 −0.085 −1.718 39.388 −2.986 3.883 39.388 0.199 −2.564 39.388 −3.288 4.724 39.388 0.476 −3.412 39.388 −3.590 5.566 39.388 0.746 −4.262 39.388 −3.882 6.380 39.388 1.000 −5.086 39.388 −4.164 7.165 39.388 1.742 −5.883 39.388 −4.433 7.924 39.388 1.472 −6.652 39.388 −4.689 8.655 39.388 1.692 −7.393 39.388 −4.932 9.360 39.388 1.905 −8.106 39.388 −5.161 10.037 39.388 2.110 −8.790 39.388 −5.375 10.689 39.388 2.309 −9.444 39.388 −5.574 11.314 39.388 2.503 −10.069 39.388 −5.746 11.884 39.388 2.674 −10.607 39.388 −5.890 12.401 39.388 2.832 −11.088 39.388 −6.010 12.863 39.388 2.985 −11.538 39.388 −6.115 13.297 39.388 3.131 −11.960 39.388 −6.203 13.675 39.388 3.258 −12.325 39.388 −6.266 13.966 39.388 3.356 −12.605 39.388 −6.311 14.200 39.388 3.436 −12.830 39.388 −6.339 14.377 39.388 3.495 −12.998 39.388 −6.352 14.510 39.388 3.540 −13.124 39.388 −6.354 14.585 39.388 3.574 −13.222 39.388 −6.350 14.632 39.388 3.593 −13.279 39.388 −6.344 14.655 39.388 3.584 −13.312 39.388 −6.337 14.665 39.388 3.573 −13.323 39.388

It will also be appreciated that the airfoil 100 disclosed in the above TABLE I may be scaled up or down geometrically for use in other similar gas turbine designs. Consequently, the coordinate values set forth in TABLE I may be scaled upwardly or downwardly such that the airfoil profile shape remains unchanged. A scaled version of the coordinates in TABLE I would be represented by X, Y and Z coordinate values, with the X, Y and Z non-dimensional coordinate values converted to units of distance (e.g., inches), multiplied or divided by a constant number (e.g. a scaling factor).

As shown in FIG. 4, each airfoil 100 may define a stagger angle α (alpha) measured between the chord line 110 and the axial direction A of the gas turbine 10. Specifically, the stagger angle α may be measured between the chord line 110 of an airfoil 100 and the axial centerline 23 (or rotary axis) of the gas turbine 10 at the trailing edge 108 of the airfoil 100. The stagger angle α of each airfoil 100 disclosed herein may advantageously vary along the span-wise direction 118 (or radial direction R) according to a respective stagger angle distribution. The stagger angle distribution may be a collection of stagger angles α for a given airfoil 100 at each span-wise location (or radial location) along the airfoil 100.

In many embodiments, each stage S1-S22 of rotor blades 44 may include a unique stagger angle distribution, such that the collective utilization of the stages S1-S22 of rotor blades 44 will yield a highly efficient compressor section 14. For example, each of the airfoils 100 of the rotor blades 44 within the first stage S1 may have a first stagger angle distribution, each of the airfoils 100 of the rotor blades 44 within the second stage S2 may have a second stagger angle distribution, and so on for each stage (S1-S22) of the compressor section 14.

Similarly, each stage S1-S22 of stator vanes 50 may include a unique stagger angle distribution, such that the collective utilization of the stages S1-S22 of stator vanes 50 will yield a highly efficient compressor section 14. For example, each of the airfoils 100 of the stator vanes 50 within the first stage S1 may have a first stagger angle distribution, each of the airfoils 100 of the stator vanes 50 within the second stage S2 may have a second stagger angle distribution, and so on for each stage (S1-S22) of the compressor section 14.

In accordance with embodiments of the present disclosure, FIG. 5 illustrates a graph of a stagger angle distribution, which may belong to one or more airfoils 100 within a specified stage (e.g., S1-S22) of the compressor section 14. Each of the graphs may be in non-dimensional units. Specifically, the y-axis may be a percentage along the span-wise direction 118 (e.g., with 0% span representing the inner diameter and 100% Y span representing the outer diameter). For example, with a rotor blade 44, 0% span may represent the base of the airfoil 100, and 100% span may represent the tip of the airfoil 100. As for a stator vane 50, 0% span may represent the tip of the airfoil 100, and 100% span may represent the base of the airfoil 100. The x-axis may be a ratio between the stagger angle at a specified span-wise location and the mid-span stagger angle (e.g., at about 50% span).

Each of the stagger angle distributions is plotted between 15% span and 85% span of the respective airfoil 100 to which it belongs (e.g., 0%-15% span and 85%-100% span points are omitted). Each stagger angle distribution, when implemented in an airfoil 100 on a rotor blade 44 and/or a stator vane 50 within the compressor section 14, advantageously increase the aerodynamic efficiency of the airfoil 100 (as well as the entire compressor section 14) when compared to prior designs.

In particular, FIG. 5 is a graph of a stagger angle distribution, plotted from 15% to 85% span of an airfoil 100 belonging to a rotor blade 44 within the first stage S1 (i.e., a first stage rotor blade). In some embodiments, all of the rotor blades 44 within the first stage S1 of the compressor section 14 may include an airfoil 100 having the stagger distribution according to FIG. 5. The stagger angle distribution shown in FIG. 5 is plotted according to the points in TABLE II below.

TABLE II Stage One Rotor Blade Airfoil (%) — Span Stagger/Midspan stagger 85.00% 1.310 79.60% 1.260 71.47% 1.188 63.18% 1.115 54.62% 1.041 45.75% 0.963 36.46% 0.875 26.66% 0.780 19.42% 0.713 15.00% 0.677

The disclosed airfoil shape optimizes and is specific to the machine conditions and specifications. It provides a unique profile to achieve 1) interaction between other stages in the compressor section 14; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings. The disclosed loci of points defined in TABLE I allow the gas turbine 10 or any other suitable turbine to run in an efficient, safe and smooth manner. As also noted, the disclosed airfoil 100 may be adapted to any scale, as long as 1) interaction between other stages in the compressor section 14; 2) aerodynamic efficiency; and 3) normalized aerodynamic and mechanical blade loadings are maintained in the scaled turbine.

The airfoil 100 described herein thus improves overall gas turbine 10 efficiency. The airfoil 100 also meets all aeromechanical and stress requirements. For example, the airfoil 100 of the rotor blade 44 thus is of a specific shape to meet aerodynamic, mechanical, and heat transfer requirements in an efficient and cost-effective manner.

This written description uses examples to disclose the invention, including the best mode, and also to enable any person skilled in the art to practice the invention, including making and using any devices or systems and performing any incorporated methods. The patentable scope of the invention is defined by the claims, and may include other examples that occur to those skilled in the art. Such other examples are intended to be within the scope of the claims if they include structural elements that do not differ from the literal language of the claims, or if they include equivalent structural elements with insubstantial differences from the literal language of the claims.

Further aspects of the invention are provided by the subject matter of the following clauses:

A rotor blade comprising an airfoil having an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value, the airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape.

The rotor blade of one or more of these clauses, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.

The rotor blade of one or more of these clauses, wherein the rotor blade forms part of a stage of a compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is disposed in one of an early stage of the compressor section, a mid stage of the compressor section, or a late stage of the compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is a first stage compressor rotor blade.

The rotor blade of one or more of these clauses, wherein the airfoil shape lies in an envelope within +/−5% of a chord length in a direction normal to any airfoil surface location.

The rotor blade of one or more of these clauses, wherein the scaling factor is between about 0.01 inches and about 10 inches.

The rotor blade of one or more of these clauses, wherein the X, Y and Z values are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

A rotor blade comprising an airfoil having a nominal suction-side profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define suction-side profile sections at each Z value, the suction-side profile sections at the Z values being joined smoothly with one another to form a complete airfoil suction-side shape.

The rotor blade of one or more of these clauses, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.

The rotor blade of one or more of these clauses, wherein the rotor blade forms part of a stage of a compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is disposed in one of an early stage of the compressor section, a mid stage of the compressor section, or a late stage of the compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is a first stage compressor rotor blade.

The rotor blade of one or more of these clauses, wherein the nominal suction-side profile lies in an envelope within +/−5% of a chord length in a direction normal to any airfoil surface location.

The rotor blade of one or more of these clauses, wherein the scaling factor is between about 0.01 inches and about 10 inches.

The rotor blade of one or more of these clauses, wherein the X, Y and Z values are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.

A turbomachine comprising a compressor section; a turbine section downstream from the compressor section; a combustion section downstream from the compressor section and upstream from the turbine section; and two or more rotor blades disposed within the compressor section of the turbomachine, each rotor blade of the two or more rotor blades comprising an airfoil having an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value, the airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape.

The turbomachine of one or more of these clauses, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.

The turbomachine of one or more of these clauses, wherein the two or more rotor blades each form part of a stage of a compressor section.

The turbomachine of one or more of these clauses, wherein each rotor blade of the two or more rotor blades is disposed in one of an early stage of the compressor section, a mid stage of the compressor section, or a late stage of the compressor section.

A rotor blade comprising an airfoil having an airfoil shape, the airfoil shape having a nominal profile, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.

The rotor blade of one or more of these clauses, wherein the rotor blade forms part of a stage of a compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is disposed in one of an early stage of the compressor section, a mid stage of the compressor section, or a late stage of the compressor section.

The rotor blade of one or more of these clauses, wherein the rotor blade is a first stage compressor rotor blade.

The rotor blade of one or more of these clauses, wherein the airfoil shape lies in an envelope within +/−5% of a chord length in a direction normal to any airfoil surface location.

The rotor blade of one or more of these clauses, wherein the scaling factor is between about 0.01 inches and about 10 inches.

The rotor blade of one or more of these clauses, wherein the nominal profile is defined substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value, the airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape, wherein the X, Y and Z values are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil. 

What is claimed is:
 1. A rotor blade comprising: an airfoil having an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value, the airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape.
 2. The rotor blade of claim 1, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.
 3. The rotor blade of claim 1, wherein the rotor blade forms part of an early stage of a compressor section of a turbomachine.
 4. The rotor blade of claim 1, wherein the rotor blade is disposed in one of a mid stage of a compressor section of a turbomachine or a late stage of the compressor section of the turbomachine.
 5. The rotor blade of claim 1, wherein the rotor blade is a first stage compressor rotor blade.
 6. The rotor blade of claim 1, wherein the airfoil shape lies in an envelope within +/−5% of a chord length in a direction normal to any airfoil surface location.
 7. The rotor blade of claim 1, wherein the scaling factor is between about 0.01 inches and about 10 inches.
 8. The rotor blade of claim 1, wherein the X, Y and Z values are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 9. A rotor blade comprising: an airfoil having a nominal suction-side profile substantially in accordance with suction-side Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a scaling factor of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define suction-side profile sections at each Z value, the suction-side profile sections at the Z values being joined smoothly with one another to form a complete airfoil suction-side shape.
 10. The rotor blade of claim 9, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.
 11. The rotor blade of claim 9, wherein the rotor blade forms part of an early stage of a compressor section of a turbomachine.
 12. The rotor blade of claim 9, wherein the rotor blade is disposed in one of a mid stage of a compressor section of a turbomachine or a late stage of the compressor section of the turbomachine.
 13. The rotor blade of claim 9, wherein the rotor blade is a first stage compressor rotor blade.
 14. The rotor blade of claim 9, wherein the nominal suction-side profile lies in an envelope within +/−5% of a chord length in a direction normal to any airfoil surface location.
 15. The rotor blade of claim 9, wherein the scaling factor is between about 0.01 inches and about 10 inches.
 16. The rotor blade of claim 9, wherein the X, Y and Z values are scalable as a function of the same constant or number to provide a scaled-up or scaled-down airfoil.
 17. A turbomachine comprising: a compressor section; a turbine section downstream from the compressor section; a combustion section downstream from the compressor section and upstream from the turbine section; and two or more rotor blades disposed within the compressor section of the turbomachine, each rotor blade of the two or more rotor blades comprising: an airfoil having an airfoil shape, the airfoil shape having a nominal profile substantially in accordance with Cartesian coordinate values of X, Y and Z set forth in Table I, the Cartesian coordinate values of X, Y, and Z being defined relative to a point data origin at a base of the airfoil, wherein the Cartesian coordinate values of X, Y and Z are non-dimensional values from 0% to 100% convertible to dimensional distances expressed in a unit of distance by multiplying the Cartesian coordinate values of X, Y and Z by a height of the airfoil in the unit of distance; and wherein X and Y values, when connected by smooth continuing arcs, define airfoil profile sections at each Z value, the airfoil profile sections at Z values being joined smoothly with one another to form a complete airfoil shape.
 18. The turbomachine of claim 17, wherein the airfoil includes a stagger angle distribution in accordance with Table II, each stagger angle in the stagger angle distribution being measured between a chord line of the airfoil and a rotary axis of the airfoil.
 19. The turbomachine of claim 17, wherein the two or more rotor blades each form part of an early stage of the compressor section.
 20. The turbomachine of claim 17, wherein each rotor blade of the two or more rotor blades is disposed in a first stage of the compressor section. 